The Reds have endured a tough start to the 2017-18 season at the back after conceding 19 times in 16 Premier League games.
The Merseyside outfit have a worse defensive record than Burnley to highlight their need for a commanding cente-half.
Dejan Lovren has been out of form in the current campaign and has made high-profile mistakes against Everton, Sevilla and Tottenham Hotspur.
Former Schalke defender Joel Matip has struggled with injury problems, while Estonia international Ragnar Klavan has struggled to convince.
Liverpool FC were heavily linked with a move to sign Virgil van Dijk in the summer transfer window but the Reds were unable to get a deal over the line.
Ex-Manchester City defender Dunne told Jurgen Klopp to invest in a new leader at the back to improve upon the underwhelming options currently at Anfield.
“Liverpool need a centre-half. The ones they’ve got are the wrong ones,” Dunne told Irish radio station Newstalk.
“They’ve not performed well. The centre-halves are a little bit mentally weak.
“They can be bullied. They can make the wrong decisions.”
Liverpool FC finished in fourth place in the Premier League table last term to secure a Champions League spot.
The Reds signed four players in the summer transfer window but left-back Andy Robertson was the only defensive recruit.
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